# A confusion in string connected to movable pulley

** So as we can see the pulley attached to the body here is a movable pulley.In Illustration (A) if the block attached to the pulley is moved in the direction of the arrow with an displacement of X meters then we can state that the pulley attached to the object via string will also move with the block by a displacement of X meters.Now,if the pulley displaces by X meters then to keep the string around the pulley tight,the string has to move by 2x meters(for this problem assume the string movement is from bottom string to top string).Now coming to the second case i.e (B),here again everything is same as it was in (A),except the bottom string.In case (A) the bottom string was parallel to horizontal(I have forgot to draw it) where as in case (B) it is making and angle theta with the horizontal.

So my question is,in case (B)if the block will displace X meters along the direction of the arrow,the pulley will also move with it,so will this time the displacement of the strings(from bottom to top) to keep the string tight around the pulley be 2x meters.

• (a) This is a geometrical question rather than a physical. (b) Assuming that the top left hand end of the string is anchored, then X m of string moves upwards over the pulley in both cases. (c) But we really do need to know where the left hand ends of the string go. How, for example is angle $\theta$ maintained? Sep 6, 2020 at 14:57
• Yes sir,the angle is maintained.Also you can assume that the bottom end of the string is attached to a small block nd the top end is attached to a rigid wall,in both case Sep 6, 2020 at 15:07
• Are you assuming that the string is of fixed length, and that the 'small block' attached to the bottom end of the string is moveable? In that case you need to draw 'before and after' diagrams for the two cases. These should give you the answers you want. Sep 6, 2020 at 15:27

If the angle is maintained, then the object will move $$X(1 + \cos \theta)$$ in the direction of the string.
If the height is maintained, then the object will move $${X(1 + \sec \theta)}$$ horizontally, along the floor.